Trivial fibrations of the multiplication maps for monads generated by the functors of order-preserving and positively homogeneous functionals

In this paper we further investigate the geometry of monads of order-preserving functionals and of positively homogeneous functionals. We prove that for any compactum X with $w(X) = \tau$ the map $\mu_F X$, where $F\in\{O,OH\}$, is homeomorphic to trivial $I^\tau$-fibration if and only if $X$ is openly generated $\chi$-homogeneous compactum.